Presence of Market Imperfections and Incentive Issues
The Effect of Taxes
Taxes and Market Imperfections Combined
Concerned with the effect of capital market decisions on security prices.
Assume: (1) investment and asset management decisions are held constant and (2) consider only debt-versus-equity financing.
Capital Structure -- The mix (or proportion) of a firm’s permanent long-term financing represented by debt, preferred stock, and common stock equity.
A Conceptual Look --Relevant Rates of Return
k i = the yield on the company’s debt
Annual interest on debt Market value of debt I B = = k i
Interest paid each and every year
Bond life is infinite
Results in the valuation of a perpetual bond
No taxes (Note: allows us to focus on just capital structure issues.)
A Conceptual Look --Relevant Rates of Return E S = = k e = the expected return on the company’s equity Earnings available to common shareholders Market value of common stock outstanding k e
Earnings are not expected to grow
100% dividend payout
Results in the valuation of a perpetuity
Appropriate in this case for illustrating the
theory of the firm
A Conceptual Look --Relevant Rates of Return O V = = k o = an overall capitalization rate for the firm Net operating income Total market value of the firm k o
V = B + S = total market value of the firm
O = I + E = net operating income = interest paid plus earnings available to common shareholders
Capitalization Rate Capitalization Rate, k o -- The discount rate used to determine the present value of a stream of expected cash flows. k o k e k i B B + S S B + S = + What happens to k i , k e , and k o when leverage, B/S, increases?
Net Operating Income Approach
Net operating income equals $1,350
Market value of debt is $1,800 at 10% interest
Overall capitalization rate is 15%
Net Operating Income Approach -- A theory of capital structure in which the weighted average cost of capital and the total value of the firm remain constant as financial leverage is changed.
Required Rate of Return on Equity
Total firm value = O / k o = $1,350 / .15 = $9,000
Market value = V - B = $9,000 - $1,800 of equity = $7,200
Required return = E / S on equity * = ( $1,350 - $180 ) / $7,200 = 16.25%
Calculating the required rate of return on equity * B / S = $1,800 / $7,200 = .25 Interest payments = $1,800 x 10%
Total firm value = O / k o = $1,350 / .15 = $9,000
Market value = V - B = $9,000 - $3,000 of equity = $6,000
Required return = E / S on equity * = ( $1,350 - $300 ) / $6,000 = 17.50%
Required Rate of Return on Equity What is the rate of return on equity if B=$3,000? * B / S = $3,000 / $6,000 = .50 Interest payments = $3,000 x 10%
B / S k i k e k o
0.00 --- 15.00% 15%
0.25 10% 16.25% 15%
0.50 10% 17.50% 15%
1.00 10% 20.00% 15%
2.00 10% 25.00% 15%
Required Rate of Return on Equity Examine a variety of different debt-to-equity ratios and the resulting required rate of return on equity. Calculated in slides 9 and 10
Required Rate of Return on Equity Capital costs and the NOI approach in a graphical representation. 0 .25 .50 .75 1.0 1.25 1.50 1.75 2.0 Financial Leverage (B / S) .25 .20 .15 .10 .05 0 Capital Costs (%) k e = 16.25% and 17.5% respectively k i (Yield on debt) k o (Capitalization rate) k e (Required return on equity)
Summary of NOI Approach
Critical assumption is k o remains constant.
An increase in cheaper debt funds is exactly offset by an increase in the required rate of return on equity.
As long as k i is constant, k e is a linear function of the debt-to-equity ratio.
Thus, there is no one optimal capital structure .
Optimal Capital Structure -- The capital structure that minimizes the firm’s cost of capital and thereby maximizes the value of the firm.
Traditional Approach -- A theory of capital structure in which there exists an optimal capital structure and where management can increase the total value of the firm through the judicious use of financial leverage.
Optimal Capital Structure: Traditional Approach Traditional Approach Financial Leverage (B / S) .25 .20 .15 .10 .05 0 Capital Costs (%) k i k o k e Optimal Capital Structure
Summary of the Traditional Approach
The cost of capital is dependent on the capital structure of the firm.
Initially, low-cost debt is not rising and replaces more expensive equity financing and k o declines.
Then, increasing financial leverage and the associated increase in k e and k i more than offsets the benefits of lower cost debt financing.
Thus, there is one optimal capital structure where k o is at its lowest point.
This is also the point where the firm’s total value will be the largest (discounting at k o ).
Total Value Principle: Modigliani and Miller (M&M)
Advocate that the relationship between financial leverage and the cost of capital is explained by the NOI approach.
Provide behavioral justification for a constant k o over the entire range of financial leverage possibilities.
Total risk for all security holders of the firm is not altered by the capital structure.
Therefore, the total value of the firm is not altered by the firm’s financing mix.
Total Value Principle: Modigliani and Miller
M&M assume an absence of taxes and market imperfections.
Investors can substitute personal for corporate financial leverage.
Market value of debt ($65M) Market value of equity ($35M) Total firm market value ($100M) Market value of debt ($35M) Market value of equity ($65M) Total firm market value ($100M)
Total market value is not altered by the capital structure (the total size of the pies are the same).
Arbitrage and Total Market Value of the Firm
Arbitrage -- Finding two assets that are essentially the same and buying the cheaper and selling the more expensive.
Two firms that are alike in every respect EXCEPT capital structure MUST have the same market value. Otherwise, arbitrage is possible.
Consider two firms that are identical in every respect EXCEPT :
Company NL -- no financial leverage
Company L -- $30,000 of 12% debt
Market value of debt for Company L equals its par value
Required return on equity -- Company NL is 15% -- Company L is 16%
NOI for each firm is $10,000
Earnings available to = E = O – I common shareholders = $10,000 - $0 = $10,000
Market value = E / k e of equity = $10,000 / .15 = $66,667
Total market value = $66,667 + $0 = $66,667
Overall capitalization rate = 15%
Debt-to-equity ratio = 0
Arbitrage Example: Company NL Valuation of Company NL
Arbitrage Example: Company L
Earnings available to = E = O – I common shareholders = $10,000 - $3,600 = $6,400
Market value = E / k e of equity = $6,400 / .16 = $40,000
Total market value = $40,000 + $30,000 = $70,000
Overall capitalization rate = 14.3%
Debt-to-equity ratio = .75
Valuation of Company L
Completing an Arbitrage Transaction
Assume you own 1% of the stock of Company L (equity value = $400).
You should :
1. Sell the stock in Company L for $400.
2. Borrow $300 at 12% interest (equals 1% of debt for Company L).
3. Buy 1% of the stock in Company NL for $666.67. This leaves you with $33.33 for other investments ($400 + $300 - $666.67).
Completing an Arbitrage Transaction Original return on investment in Company L $400 x 16% = $64
Return on investment after the transaction
$666.67 x 16% = $100 return on Company NL
$300 x 12% = $36 interest paid
$64 net return ( $100 - $36 ) AND $33.33 left over .
This reduces the required net investment to $366.67 to earn $64.
Summary of the Arbitrage Transaction
The equity share price in Company NL rises based on increased share demand.
The equity share price in Company L falls based on selling pressures.
Arbitrage continues until total firm values are identical for companies NL and L.
Therefore, all capital structures are equally as acceptable.
The investor uses “personal” rather than corporate financial leverage.
Market Imperfections and Incentive Issues
Agency costs (Slide 28)
Debt and the incentive to manage efficiently
Bankruptcy costs (Slide 27)
Required Rate of Return on Equity with Bankruptcy Financial Leverage (B / S) R f Required Rate of Return on Equity (k e ) k e with no leverage k e without bankruptcy costs k e with bankruptcy costs Premium for financial risk Premium for business risk Risk-free rate
Monitoring includes bonding of agents, auditing financial statements, and explicitly restricting management decisions or actions.
Costs are borne by shareholders (Jensen & Meckling).
Monitoring costs, like bankruptcy costs, tend to rise at an increasing rate with financial leverage.
Agency Costs -- Costs associated with monitoring management to ensure that it behaves in ways consistent with the firm’s contractual agreements with creditors and shareholders.
Example of the Effects of Corporate Taxes
Consider two identical firms EXCEPT :
Company ND -- no debt, 16% required return
Company D -- $5,000 of 12% debt
Corporate tax rate is 40% for each company
NOI for each firm is $10,000
The judicious use of financial leverage (i.e., debt) provides a favorable impact on a company’s total valuation .
Earnings available to = E = O - I common shareholders = $2,000 - $0 = $2,000
Tax Rate ( T ) = 40%
Income available to = EACS (1 - T ) common shareholders = $2,000 (1 - .4 ) = $1,200
Total income available to = EAT + I all security holders = $1,200 + 0 = $1,200
Corporate Tax Example: Company ND Valuation of Company ND (Note: has no debt)
Earnings available to = E = O - I common shareholders = $2,000 - $600 = $1,400
Tax Rate ( T ) = 40%
Income available to = EACS (1 - T ) common shareholders = $1,400 (1 - .4 ) = $840
Total income available to = EAT + I all security holders = $840 + $600 = $1,440 *
Corporate Tax Example: Company D Valuation of Company D (Note: has some debt) * $240 annual tax-shield benefit of debt (i.e., $1,440 - $1,200)
Tax-Shield Benefits Tax Shield -- A tax-deductible expense. The expense protects (shields) an equivalent dollar amount of revenue from being taxed by reducing taxable income. Present value of tax-shield benefits of debt * = ( r ) ( B ) ( t c ) r = ( B ) ( t c ) * Permanent debt, so treated as a perpetuity ** Alternatively, $240 annual tax shield / .12 = $2,000, where $240=$600 Interest expense x .40 tax rate. = ( $5,000 ) ( .4 ) = $2,000 **
Value of the Levered Firm
Value of unlevered firm = $1,200 / .16 (Company ND) = $7,500 *
Value of levered firm = $7,500 + $2,000 (Company D) = $9,500
Value of Value of Present value of levered = firm if + tax-shield benefits firm unlevered of debt * Assuming zero growth and 100% dividend payout
Summary of Corporate Tax Effects
The greater the financial leverage, the lower the cost of capital of the firm.
The adjusted M&M proposition suggests an optimal strategy is to take on the maximum amount of financial leverage .
This implies a capital structure of almost 100% debt! Yet, this is not consistent with actual behavior.
The greater the amount of debt, the greater the tax-shield benefits and the greater the value of the firm.
Other Tax Issues
Corporate plus personal taxes
Personal taxes reduce the corporate tax advantage associated with debt.
Only a small portion of the explanation why corporate debt usage is not near 100%.
Uncertainty of tax-shield benefits
Uncertainty increases the possibility of bankruptcy and liquidation, which reduces the value of the tax shield.
Bankruptcy Costs, Agency Costs, and Taxes
As financial leverage increases, tax-shield benefits increase as do bankruptcy and agency costs .
Value of levered firm = Value of firm if unlevered + Present value of tax-shield benefits of debt - Present value of bankruptcy and agency costs
Bankruptcy Costs, Agency Costs, and Taxes Optimal Financial Leverage Taxes, bankruptcy, and agency costs combined Net tax effect Financial Leverage (B/S) Cost of Capital (%) Minimum Cost of Capital Point
Informational Asymmetry is based on the idea that insiders (managers) know something about the firm that outsiders (security holders) do not.
Changing the capital structure to include more debt conveys that the firm’s stock price is undervalued .
This is a valid signal because of the possibility of bankruptcy.
A manager may use capital structure changes to convey information about the profitability and risk of the firm.